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# m-mujica/equilibrium_index

Created Mar 20, 2014
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 A zero-indexed array A consisting of N integers is given. An equilibrium index of this array is any integer P such that 0 ≤ P < N and the sum of elements of lower indices is equal to the sum of elements of higher indices, i.e. A[0] + A[1] + ... + A[P−1] = A[P+1] + ... + A[N−2] + A[N−1]. Sum of zero elements is assumed to be equal to 0. This can happen if P = 0 or if P = N−1. For example, consider the following array A consisting of N = 7 elements: A[0] = -7 A[1] = 1 A[2] = 5 A[3] = 2 A[4] = -4 A[5] = 3 A[6] = 0 P = 3 is an equilibrium index of this array, because: A[0] + A[1] + A[2] = A[4] + A[5] + A[6] P = 6 is also an equilibrium index, because: A[0] + A[1] + A[2] + A[3] + A[4] + A[5] = 0 and there are no elements with indices greater than 6. P = 7 is not an equilibrium index, because it does not fulfill the condition 0 ≤ P < N. Write a function function solution(A); that, given a zero-indexed array A consisting of N integers, returns any of its equilibrium indices. The function should return −1 if no equilibrium index exists. Assume that: N is an integer within the range [0..10,000,000]; each element of array A is an integer within the range [−2,147,483,648..2,147,483,647]. For example, given array A such that A[0] = -7 A[1] = 1 A[2] = 5 A[3] = 2 A[4] = -4 A[5] = 3 A[6] = 0 the function may return 3 or 6, as explained above. Complexity: expected worst-case time complexity is O(N); expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments). Elements of input arrays can be modified.